pyemma.msm.tpt¶
-
pyemma.msm.
tpt
(msmobj, A, B)¶ A->B reactive flux from transition path theory (TPT)
The returned
ReactiveFlux
object can be used to extract various quantities of the flux, as well as to compute A -> B transition pathways, their weights, and to coarse-grain the flux onto sets of states.Parameters: - msmobj (
MSM
object) – Markov state model (MSM) object - A (array_like) – List of integer state labels for set A
- B (array_like) – List of integer state labels for set B
Returns: tptobj – An object containing the reactive A->B flux network and several additional quantities, such as the stationary probability, committors and set definitions.
Return type: ReactiveFlux
objectSee also
ReactiveFlux
- Reactive Flux model
References
Transition path theory was introduced for space-continuous dynamical processes, such as Langevin dynamics, in [1]_, [2]_ introduces discrete transition path theory for Markov jump processes (Master equation models, rate matrices) and pathway decomposition algorithms. [3]_ introduces transition path theory for Markov state models (MSMs) and some analysis algorithms. In this function, the equations described in [3]_ are applied.
[1] W. E and E. Vanden-Eijnden. Towards a theory of transition paths. J. Stat. Phys. 123: 503-523 (2006) [2] P. Metzner, C. Schuette and E. Vanden-Eijnden. Transition Path Theory for Markov Jump Processes. Multiscale Model Simul 7: 1192-1219 (2009) [3] F. Noe, Ch. Schuette, E. Vanden-Eijnden, L. Reich and T. Weikl: Constructing the Full Ensemble of Folding Pathways from Short Off-Equilibrium Simulations. Proc. Natl. Acad. Sci. USA, 106, 19011-19016 (2009) Computes the A->B reactive flux using transition path theory (TPT)
Parameters: - T ((M, M) ndarray or scipy.sparse matrix) – Transition matrix (default) or Rate matrix (if rate_matrix=True)
- A (array_like) – List of integer state labels for set A
- B (array_like) – List of integer state labels for set B
- mu ((M,) ndarray (optional)) – Stationary vector
- qminus ((M,) ndarray (optional)) – Backward committor for A->B reaction
- qplus ((M,) ndarray (optional)) – Forward committor for A-> B reaction
- = False (rate_matrix) – By default (False), T is a transition matrix. If set to True, T is a rate matrix.
Returns: tpt – A python object containing the reactive A->B flux network and several additional quantities, such as stationary probability, committors and set definitions.
Return type: msmtools.flux.ReactiveFlux object
Notes
The central object used in transition path theory is the forward and backward comittor function.
TPT (originally introduced in [1]) for continous systems has a discrete version outlined in [2]. Here, we use the transition matrix formulation described in [3].
See also
References
[1] W. E and E. Vanden-Eijnden. Towards a theory of transition paths. J. Stat. Phys. 123: 503-523 (2006) [2] P. Metzner, C. Schuette and E. Vanden-Eijnden. Transition Path Theory for Markov Jump Processes. Multiscale Model Simul 7: 1192-1219 (2009) [3] F. Noe, Ch. Schuette, E. Vanden-Eijnden, L. Reich and T. Weikl: Constructing the Full Ensemble of Folding Pathways from Short Off-Equilibrium Simulations. Proc. Natl. Acad. Sci. USA, 106, 19011-19016 (2009) - msmobj (